# What is the standard form of the equation of the parabola with a directrix at #x=9# and a focus at #(8,4)#?

##### 1 Answer

The standard form is:

#### Explanation:

Because the directrix is a vertical line, one knows that the vertex form of the equation for the parabola is:

where

The x coordinate of the vertex halfway between the directrix and the focus :

Substitute into equation [1]:

The y coordinate of the vertex is the same as the y coordinate of the focus:

Substitute into equation [2]:

The value of

Substitute into equation [3]:

This is the vertex form:

Expand the square:

Use the distributive property:

Combine like terms:

Here is a graph of the standard form, the focus, the vertex, and the directrix: